source : yahoo.com
Which equation implies that A and B are independent events?
If A and B are independent events, that means the likelihood of one event happening is independent of the other event happening. The outcomes do not depend on each other and are unaffected by the other outcome.
A = rolling a die and getting a 2
B = flipping a coin and getting heads
These events are independent because whatever you roll on the die doesn’t affect what might happen with the coin toss.
With independent events, the probability of both events happening is simply the product.
P(A and B) = P(A) x P(B)
P(A) = 1/6 <– rolling a 2
P(B) = 1/2 <– flipping heads
P(A and B) = 1/6 x 1/2 = 1/12 <– rolling a 2 and flipping heads
Dependent and Independent Events – Alexander Bogomolny – It implies. P(B) = P(A∩B)/P(A) = P(B|A), which exactly means that B is independent of A. We see that two events A and B are either both dependent or independent one from the other. The symmetric definition of independency is this (*) P(A∩B) = P(A) P(B). Two events A and B are independent iff that condition holds. They are dependent otherwise.If A and B are independent events, then the events A and B' are also independent. Proof: The events A and B are independent, so, P(A ∩ B) = P(A) P(B). From the Venn diagram, we see that the events A ∩ B and A ∩ B' are mutually exclusive and together they form the event A. A = ( A ∩ B) ∪ (A ∩ B').B = flipping a coin and getting heads These events are independent because whatever you roll on the die doesn't affect what might happen with the coin toss. With independent events, the probability…
Independent Events – Toppr-guides – It is given that both the events A and B are independent with their respective probabilities P (A)=0.6 and P (B)=0.4. As they are independent, product of their probabilities is the probability of occurring of both events simultaneously i.e. P (A and B)=P (A)*P (B) So we have P (A and B)= 0.6*0.4=0.24 According to the addition law of probabilityTwo events A and B are independent iff P (A∩B) = P (A)P (B). This definition extends to the notion of independence of a finite number of events. Let K be a finite set of indices. Events A k, k∈K are said to be mutually (or jointly) independent iffIn other words, A and B being disjoint events implies that if event A occurs then B does not occur and vice versa. Well… if that's the case, knowing that event A has occurred dramatically changes the likelihood that event B occurs – that likelihood is zero. This implies that A and B are not independent.
Which equation implies that A and B are independent events – Sometimes this formula is used as the definition of independent events. Events are independent if and only if P (A and B) = P (A) x P (B). Example #1 of the Use of the Multiplication Rule We will see how to use the multiplication rule by looking at a few examples.gradient23's proof is great, in my opinion, but I would like to show another proof that seems more intuitive to me, though much less rigorous.. The proof is based on a verbal definition of independence from wikipedia:. two events are independent […] if the occurrence of one does not affect the probability of occurrence of the otherAnother equation used for independent events is P (B | A) = P (B). When the multiplication rule is applied, this gives an alternative definition of independence which is: P (A ∩ B) = P (A)*P (B) Independent events are events that can occur without affecting or changing the probability of the other.